1) Consider the case of LiH which has an average bond distance of 159.5 pm. Given this constraint for the bond distance, evaluate the optimum geometry for the triatomic molecule Li2H+. More specifically, assume that the two LiH bond lengths are fixed and that the interactions between the ions Li+ and H- are strictly electrostatic. Vary the angle of [Li-H-Li]+. Make a plot of the change in the energy as a function of the angle. Provide a physical explanation for the answer that you find.

Please include a labeled graph that includes tick marks with values, and axis labels with units.

2)Given the expression for the energy of an electron trapped in a one-dimensional box, describe how the energy changes with the size of the box. Make a plot that shows this dependence for n=1, n=2, and n=3. Based on your findings describe how you would expect the electronic energy levels of a chain of hydrogen atoms to change as the number of atoms in the chain is increased? Remember that as you increase the number of atoms in the chain, you are increasing the box length and the number of electrons.

Please include a labeled graph that includes tick marks with values, and axis labels with units.

3)When an electron is bound to a proton it makes a hydrogen atom, for which the accepted atomic diameter is 128 pm.

a.) Estimate the largest wavelength that an electron could have if it were trapped inside of a box of this size, assume that the wave has to go to zero at the boundaries of the box. From this wavelength calculate the average kinetic energy.

b.) Perform an estimation similar to that of part a.) but perform it for an electron that is confined in:

i.) A benzene ring

ii.) a C60 molecule

iii.) a 10 nm diameter Au colloid

Estimate the diameters of benzene and C60 by using their density and molecular weights.

c.) Based on your calculations, discuss how you expect the kinetic energy of an electron to change as you change its ability to delocalize throughout a molecule or other nanometer sized particle.